The Completeness of Quantum Mechanics Truong Pham Copenhagen
- Slides: 20
The Completeness of Quantum Mechanics Truong Pham
Copenhagen Interpretation(s) �
Copenhagen Interpretation(s)
Copenhagen Interpretation(s) �
Superposition and Measurement � Ψ: state of a particle � Φ: state of a measuring device � Ψ(+) : state of a particle that has an upspin � Ψ(-): state of a particle that has a downspin � Φ(+): state of a measuring device corresponding to an upspin � Φ(-): state of a measuring device corresponding to a downspin
Two possible interpretations � Born: the possibility of getting upspin and downspin is m^2 and n^2, respectively � Heisenberg: the state of the total system is a superposition between the upspin and the downspin states. Once observation is made, the system is collapsed to one state
Schrodinger’s kitty
Superposition analysis: � P=mΨ(live)* Φ(atom)+nΨ(dead) Φ(decay) � Born: probabilities for the kitty to be alive and dead are m^2 and n^2, respectively. � Heisenberg: the kitty is in a superposition of dead and alive states before one opens the box � Einstein: “Both points of view are logically unobjectionable; but I cannot believe that either of these viewpoints will finally be established. ” (Cushing, 312)
Einstein’s argument � 1. Born is right -> incompleteness of QM. � 2. Heisenberg is right -> the cat’s actual physical state before observation is actually a superposition of death and life -> the mere act of observing either kills or let the cat live on � 2 does not sound right (Or does it? ). � Therefore 1: QM is an incomplete theory.
Quantum Entanglement SPOOKY!
EPR paradox � EPR paper was coauthored by Einstein, Podolsky and Rosen. � Modified by David Bohm � Basis for hidden variables theory: Distant events cannot have instantaneous effect on local ones.
Simplified schematic diagram P=mΨ(+)* Φ(+)+nΨ(-) Φ(-)
� If particle 1’s spin is observed to be up, particle 2 has to have a downspin. � Vice versa � Merely observing 1 particle changes the state of the other. � Two particles can be infinitely far away from each other � -> Information travels faster than light?
Bell’s theorem �A set of inequalities to prove that in some cases, local hidden variables theory cannot be satisfied � Verified by experiment that entanglement does indeed happen � But does information actually travels faster than light in violation of general relativity?
Niels Bohn � No � If we consider 2 particles as a system � The overall wave function for the system collapses when we make an observation � Just like the Schrodinger’s cat � No information transmission takes place
David Bohm � Na ah, � Non-local hidden-variables theory
New Developments � Speed of information transmission was measured to be at least 10, 000 times greater than the speed of light! � Quantum computing
Discussion � Which interpretation is realist? Or is Quantum Mechanics essentially instrumentalist? � Einstein and Bohn’s conversation: E: Do you realistically believe that the Moon does not exist if nobody is looking at it? B: You cannot disprove that…
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